Optimal Transforms for Multispectral and Multilayer Image Coding y

1 Multispectral images are composed of a series of images at di ering optical wavelengths. Since these images can be quite large, they invite e cient source coding schemes for reducing storage and transmission requirements. Because multispectral images include a third (spectral) dimension with nonstationary behavior, these multilayer data sets require specialized coding techniques. In this paper, we develop both a theory and speci c methods for performing optimal transform coding of multispectral images. The theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary Gaussian random processes. Therefore, the methods may be applied to any multilayer data set which meets this assumption. Although we do not assume the autocorrelation has a separable form, we show that the optimal transform for coding has a partially separable structure. In particular, we prove that a coding scheme consisting of a frequency transform within each layer followed by a separate KL transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large. Two simpli cations of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints. The proposed coding techniques are then implemented using subband ltering methods, and the various algorithms are tested on multispectral images to determine their relative performance characteristics. IP EDICS #1.1 Image Processing: Coding This work was supported by an AT&T Bell Laboratories PhD Scholarship and an NEC Faculty Fellowship. Permission to publish this abstract separately is granted.